共查询到19条相似文献,搜索用时 62 毫秒
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本文在一般的Banach空间中研究非凸微分包含的生存问题.我们首先构造出了上述非凸微分包含的一个生存集.然后给出了所构造的生存集的两个应用. 相似文献
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凸性与度量投影的连续性 总被引:9,自引:0,他引:9
本文研究近强凸、近非常凸Banach空间中度量投影的连续性。获得如下结果:若A是近强凸(近非常凸)空间中的逼近凸集,则度量投影PA是范-范上半连续的(范-弱上半连续的)。此外,我们还利用度量投影的连续性给出Banach空间为近强凸、近非常凸的一些充分必要条件。 相似文献
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为研究度量线性空间中凸集的逼近性质,G.C.Ahuja等引起了度量线性空间的严格凸性及一致凸性的定义。本文证明了完备的一致凸的度量线性空间是自反的。同时,作为应用,研究了最佳联合逼近元的存在性与唯一性问题。 相似文献
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紧—凸性与紧—光滑性 总被引:3,自引:0,他引:3
本文首先通过暴露集和暴露泛函的概念引入卫闭凸集的紧-严格凸、紧-强凸、紧-一致凸及紧-非常凸等概念。用对偶映射给出了Banach空间的两种新光滑性-紧-一致光滑与紧-非常光滑。然后特别研究了Banach空间的紧-非常凸与紧-非常光滑。此外还得到关于对偶映射的两个新结果。 相似文献
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本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的一个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱于J.-P.Aubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.-P.Aubin与H.Frankowska的结果给出一个新的简单证明,最后用反例说明本文给出的条件与J.-P.Aubin与H.Frankowska条件都是充分而不必要的. 相似文献
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研究了广义凸Fuzzy集和广义反凸Fuzzy集以及它们的性质。通过将凸Fuzzy集和E-凸集相结合,提出了一种新的广义凸Fuzzy集———E-凸Fuzzy集,使得凸Fuzzy集成为它的特例,并对E-凸Fuzzy集的性质进行了初步研究。然后,类似地,通过将反凸Fuzzy集和E-凸集相结合,提出了一种新的广义反凸Fuzzy集———E-反凸Fuzzy集,使得反凸Fuzzy集成为它的特例,并对E-反凸Fuzzy集的性质进行了初步研究。 相似文献
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K-Drop凸空间与局部K-Drop凸空间 总被引:1,自引:0,他引:1
引入了Banach空间的局部k-drop凸性质,研究了k-drop凸与局部k-drop凸的一些性质以及两者之间的关系,并用单位球的切片统一而简洁地处理了这两个性质. 相似文献
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Truong Xuan Duc Ha 《Optimization》2019,68(7):1321-1335
AbstractThis short paper characterizes strictly convex sets by the uniqueness of support points (such points are called unique support points or exposed points) under appropriate assumptions. A class of so-called regular sets, for which every extreme point is a unique support point, is introduced. Closed strictly convex sets and their intersections with some other sets are shown to belong to this class. The obtained characterizations are then applied to set-valued maps and to the separation of a convex set and a strictly convex set. Under suitable assumptions, so-called set-valued maps with path property are characterized by strictly convex images of the considered set-valued map. 相似文献
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主要研究了两类近似凸集的关系和性质.首先,举例说明两类近似凸集没有相互包含关系.其次,在近似凸集(nearly convex)条件下,证明了在一定条件下函数上图是近似凸集与凸集的等价关系.同时,考虑了近似凸函数与函数上图是近似凸集的等价刻画、近似凸函数与函数水平集是近似凸集的必要性,并用例子说明近似凸函数与函数水平集是近似凸集的充分性不成立.最后,基于近似凸函数和拟凸函数的概念,给出了近似拟凸函数的概念并研究了近似拟凸函数与水平集是近似凸集的等价刻画. 相似文献
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Domingo García Ond?ej F.K. Kalenda Manuel Maestre 《Journal of Mathematical Analysis and Applications》2010,363(2):663-678
We investigate certain envelopes of open sets in dual Banach spaces which are related to extending holomorphic functions. We give a variety of examples of absolutely convex sets showing that the extension is in many cases not possible. We also establish connections to the study of iterated weak∗ sequential closures of convex sets in the dual of separable spaces. 相似文献
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Caixing Gu Jonathan E. Shapiro 《Proceedings of the American Mathematical Society》2003,131(9):2779-2789
We find some extreme points in the unit ball of the set of Hankel operators and show that the unit ball of the set of compact Hankel operators is strictly convex. We use this result to show that the collection of lower triangular Toeplitz contractions is strictly convex. We also find some extreme points in certain reduced Cowen sets and discuss cases in which they are or are not strictly convex.
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《Set-Valued Analysis》2008,16(2-3):307-318
In this paper we study a class of closed convex sets introduced recently by Ernst et al. (J Funct Anal 223:179–203, 2005) and called by these authors slice-continuous sets. This class, which plays an important role in the strong separation of
convex sets, coincides in ℝ
n
with the well known class of continuous sets defined by Gale and Klee in the 1960s. In this article we achieve, in the setting
of reflexive Banach spaces, two new characterizations of slice-continuous sets, similar to those provided for continuous sets
in ℝ
n
by Gale and Klee. Thus, we prove that a slice-continuous set is precisely a closed and convex set which does not possess
neither boundary rays, nor flat asymptotes of any dimension. Moreover, a slice-continuous set may also be characterized as
being a closed and convex set of non-void interior for which the support function is continuous except at the origin.
Dedicated to Boris Mordukhovich in honour of his 60th birthday. 相似文献
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On the convergence of the coordinate descent method for convex differentiable minimization 总被引:3,自引:0,他引:3
The coordinate descent method enjoys a long history in convex differentiable minimization. Surprisingly, very little is known about the convergence of the iterates generated by this method. Convergence typically requires restrictive assumptions such as that the cost function has bounded level sets and is in some sense strictly convex. In a recent work, Luo and Tseng showed that the iterates are convergent for the symmetric monotone linear complementarity problem, for which the cost function is convex quadratic, but not necessarily strictly convex, and does not necessarily have bounded level sets. In this paper, we extend these results to problems for which the cost function is the composition of an affine mapping with a strictly convex function which is twice differentiable in its effective domain. In addition, we show that the convergence is at least linear. As a consequence of this result, we obtain, for the first time, that the dual iterates generated by a number of existing methods for matrix balancing and entropy optimization are linearly convergent.This work was partially supported by the U.S. Army Research Office, Contract No. DAAL03-86-K-0171, by the National Science Foundation, Grant No. ECS-8519058, and by the Science and Engineering Research Board of McMaster University. 相似文献
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Generalized polyhedral convex sets, generalized polyhedral convex functions on locally convex Hausdorff topological vector spaces, and the related constructions such as sum of sets, sum of functions, directional derivative, infimal convolution, normal cone, conjugate function, subdifferential are studied thoroughly in this paper. Among other things, we show how a generalized polyhedral convex set can be characterized through the finiteness of the number of its faces. In addition, it is proved that the infimal convolution of a generalized polyhedral convex function and a polyhedral convex function is a polyhedral convex function. The obtained results can be applied to scalar optimization problems described by generalized polyhedral convex sets and generalized polyhedral convex functions. 相似文献